When engineering students are unable to evaluate the validity of their solutions, they are unprepared to solve complex, real-world engineering problems that require decomposition or knowledge transfer. A proper framework is key to successful implementation and can encourage more institutions to adopt problem-solving engineering labs. This paper documents a design framework the authors developed to create different mechanical engineering problem-solving lab modules. The framework offers a systematic approach for educators to strategically plan, create, and execute a series of interconnected laboratory activities spanning multiple weeks. The methodology aims to reinforce students' understanding of previously learned engineering principles by applying them to address practical issues associated with grand engineering challenges or daily problems. A three-credit, fourth-year laboratory course was designed to follow a Revised Bloom's taxonomy hierarchy (Remember, Understand, Apply, Analyze, Evaluate, and Create) to improve students' metacognition skills when problem-solving. This paper focuses on the detailed course design of a three-week module in the mid-semester within that larger course, emphasizing two cognitive skills: Analysis and Evaluation. Two case studies are presented, each addressing a real-world engineering problem to capture students' interest. At various stages of each lab module, survey data was collected to evaluate student perception in applying critical thinking skills when problem-solving. The majority of students felt the labs demonstrated real-world applications to the respective engineering topics across the mechanical engineering curriculum and encouraged them to apply analytical skills to solve problems.